We propose and experimentally demonstrate a hybrid fiber optic sensing technique that effectively combines Brillouin optical time-domain analysis and a time-domain multiplexing interrogation technique for Fiber Bragg Gratings (FBGs). The highly-integrated proposed scheme employs broadband apodized low-reflectivity FBGs with a single optical source and a shared receiver block, allowing for simultaneous measurements of distributed static and discrete dynamic temperature and strain, over the same sensing fiber.